Is there any downside to using Heightened spells in place of regular ones?
It takes up a higher level spell slot. For example, a Fireball Heightened to a 4th level spell takes up a 4th level slot, not a 3rd level one. However, everything else remains the same (max damage cap, etc.).
Heighten is useful for penetrating things like Globe of Invulnerability, increasing spell DC (it is a 4th level spell, so DC is 14+casting stat bonus for that Fireball example) and for certain PrC qualifying shenannigans, but other than that, not really.